374 On the Lmv,s of Inheritance in Man 



shown by tlie sensible correlatiou thore is in eye-colonr between hii.sband and 

 wife, i.e. •10+04*, which is closely in agreenient with the results for stature of 

 husband aud wife from the same data. 



We niay, however, estimate how far matiog with regard to .«tatnre would 

 produce reseniblanccs in span and forearni. Let the snbsc-ripts 1, 3, 5 refer to 

 tln'ee organs in a male of the population who marries, and 2, 4, 6 to the corre- 

 sponding organs of a female of the marrying part of the population. Then 

 ^13, ^s5. 'n I 'm. '"le, '■« are organic correlations such as we have tabled on p. 370. All 

 correlatioiis such as ?',g, r„, ?',o, »Vj. '"m. ''ss. »'k, 'm. 'm are zero, if we niated pairs at 

 random. Now let them be assortatively raated and let p,2, p^, p^ represent the 

 degree of rescmblance in the sexual selection. Let rj«, r«, r„ be the apparent 

 correlations of mated pairs ; then Tjo will not be equal to p^^, for it is partly due 

 to the degree of assortative mating indicated in p^ and p«, because 3 and 5 

 are organically correlated with 1, and 4 and G with 2; thus the selection of 3's 

 and o's to associate with 4's and 6's would indircctly influence the relationship 

 of 1 and 2, even if there were uo direct associating of l's and 2's. The relationship 

 of r,2, Tsj, rjg to p,2, ps,, Pb8 may be easily found from my memoir on the influence of 

 selection on variability and correlatiou f. We have only to put in the formulae of 

 pp. 15 — 17 tlie appropriate values for the population described above and we find : 



(i). 



Tu = py, + p^ r,3 Toi + pM »'ir, '^6 



»"34 = Pli »U »"24 + Pw +PX '"m »'o. 



^x ^ Pn ^15 '"sB + Pu ''35 ''41! + Pss 



Now suppose that 1 and 2 represent statures, 3 and 4 spans, aud 5 and 6 

 forearms. Then if all assortative mating be due to selection of stature, we might 

 put Pjj and p^ zero above and we should have : 



P12 ^^ ^\t> ^U — ^^12 '13 'm ) ^M — rij?'i5?'26. 



But Tis = -7829, r.^ = -7000, r„ = 0397, r.^ = -0968, and r,., =-2804. This leads to 



räi=166() and rj,.,=i071, 



as against the observed values : 



r». = -19>s9 and T^=wn. 



The former values are too sniall in both cases and, I think, we ma}' safely 

 assert, that the likeness of husband and wife in forearm and span is not solely 

 due to a selection of stature. 



Another explanation of the.se high coefficients of assortative mating has been 

 suggested to me, naniely that the population of England is built up of a nuniber 



* Phil. Trans. Vol. 195, A, p. 113. See also pp. 148 — 150, wherc it is shown that lieterogaiiiy rnther 

 than homoRam}' in eyc-colour tends to iucreased fertility. If tbis be coufirmcd, eyc-colour differs much 

 in effect from stature. 



t Phil. Tran». Vol. 200, p. 1 et seq. 



